Ullemar’s formula for the moment map, II

AbstractWe prove the complex analogue of Ullemar’s formula for the Jacobian of the complex moment mapping. This formula was previously established in the real case

Minimal cubic cones via Clifford algebras

We construct two infinite families of algebraic minimal cones in $R^{n}$. The first family consists of minimal cubics given explicitly in terms of the Clifford systems. We show that the classes of congruent minimal cubics are in one to one correspondence with those of geometrically equivalent Clifford systems. As a byproduct, we prove that for any $n\ge4$, $n\ne 16k+1$, there is at least one minimal cone in $R^{n}$ given by an irreducible homogeneous cubic polynomial. The second family consists of minimal cones in $R^{m^2}$, $m\ge2$, defined by an irreducible homogeneous polynomial of degree $m$. These examples provide particular answers to the questions on algebraic minimal cones posed by Wu-Yi Hsiang in the 1960's.Comment: Final version, corrects typos in Table

Disjoint minimal graphs

We prove that the number s(n) of disjoint minimal graphs supported on domains in R^n is bounded by e(n+1)^2. In the two-dimensional case we show that s(2) is at most three (the conjectured number is two).Comment: 14 page

The resultant on compact Riemann surfaces

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.Comment: 44 page

M1 Resonances in Unstable Magic Nuclei

Within a microscopic approach which takes into account RPA configurations, the single-particle continuum and more complex $1p1h\otimes phonon$ configurations isoscalar and isovector M1 excitations for the unstable nuclei ${56,78}$Ni and ${100,132}$Sn are calculated. For comparison, the experimentally known M1 excitations in ${40}$Ca and $^{208}$Pb have also been calculated. In the latter nuclei good agreement in the centroid energy, the total transition strength and the resonance width is obtained. With the same parameters we predict the magnetic excitations for the unstable nuclei. The strength is sufficiently concentrated to be measurable in radioactive beam experiments. New features are found for the very neutron rich nucleus ${78}$Ni and the neutron deficient nucleus ${100}$Sn.Comment: 17 pages (LATEX), 12 figures (available from the authors), KFA-IKP(TH)-1993-0

Modernization of the multipurpose accelerating system VGIK-1

The aim of VGIK-1 modernization is the possibility of metal surface processing by ion and electron irradiation, widening a range of applied energies and beam densities, vacuum condition control. This is reached by usage of two diodes, where one of them has isolated and defocussing magnetic system and another one has plasma emitter for extraction of ions and electrons. There is also the system of plasma parameters control. Vacuum system includes the cryogenic, diffusion and titanium sorbtion pumps and mass-spectrometric syste

The phylodynamics of the rabies virus in the Russian Federation

Near complete rabies virus N gene sequences (1,110 nt) were determined for 82 isolates obtained from different regions of Russia between 2008 and 2016. These sequences were analyzed together with 108 representative GenBank sequences from 1977-2016 using the Bayesian coalescent approach. The timing of the major evolutionary events was estimated. Most of the isolates represented the steppe rabies virus group C, which was found over a vast geographic region from Central Russia to Mongolia and split into three groups (C0-C2) with discrete geographic prevalence. A single strain of the steppe rabies virus lineage was isolated in the far eastern part of Russia (Primorsky Krai), likely as a result of a recent anthropogenic introduction. For the first time the polar rabies virus group A2, previously reported in Alaska, was described in the northern part of European Russia and at the Franz Josef Land. Phylogenetic analysis suggested that all currently circulating rabies virus groups in the Russian Federation were introduced within the few last centuries, with most of the groups spreading in the 20th century. The dating of evolutionary events was highly concordant with the historical epidemiological data. © 2017 Deviatkin et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

The phylodynamics of the rabies virus in the Russian Federation

Near complete rabies virus N gene sequences (1,110 nt) were determined for 82 isolates obtained from different regions of Russia between 2008 and 2016. These sequences were analyzed together with 108 representative GenBank sequences from 1977-2016 using the Bayesian coalescent approach. The timing of the major evolutionary events was estimated. Most of the isolates represented the steppe rabies virus group C, which was found over a vast geographic region from Central Russia to Mongolia and split into three groups (C0-C2) with discrete geographic prevalence. A single strain of the steppe rabies virus lineage was isolated in the far eastern part of Russia (Primorsky Krai), likely as a result of a recent anthropogenic introduction. For the first time the polar rabies virus group A2, previously reported in Alaska, was described in the northern part of European Russia and at the Franz Josef Land. Phylogenetic analysis suggested that all currently circulating rabies virus groups in the Russian Federation were introduced within the few last centuries, with most of the groups spreading in the 20th century. The dating of evolutionary events was highly concordant with the historical epidemiological data. © 2017 Deviatkin et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited